If average of 20 observations x1, x2, ....., x20 is y, then

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If average of 20 observations x₁, x₂, ....., x₂₀ is y, then the average of x₁ – 101, x₂ – 101, x₃ – 101, ....., x₂₀ –101 is

Given Here , average of 20 observations x₁, x₂, ....., x₂₀ = y
Now , we have

Required average =	{ ( x₁ - 101 ) + ( x₂ - 101 ) + . . . . + ( x₂₀ - 101 ) }
	20

Required average =	{ x₁ + x₂ + . . . . +x₂₀ } - { 101 × 20 }
	20

Required average =	x₁ + x₂ + . . . . +x₂₀	-	101 × 20
	20		20

Hence , Required average = y - 101